IDAX.SKEWNESS_AGG - Calculate the skewness
Use this aggregation function to calculate the skewness of a single numeric variable. Skewness measures the symmetry or rather the lack of symmetry of the data distribution. A distribution is symmetric when the left side of the distribution mirrors the right side of the distribution.
Authorization
The privileges held by the authorization ID of the statement must include the IDAX_USER role.
Syntax
IDAX.SKEWNESS_AGG(in x DOUBLE)Details
Skewness is calculated as the third central moment divided by the cube of the standard deviation.
If the skewness is positive, the tail on the right side of the probability density function might be longer than the one on the left side. In other words, most of the values probably lie to the left of the mean value.
If the skewness is negative, the tail on the left side of the probability density function might be longer than the one on the right side. In other words, most of the values probably lie to the right side of the mean value.
Normal distribution has a skewness of 0 because its probability density function is symmetric around the mean. A k-th order central moment is the sum of the k-th powers of differences between the mean and the actual value that is divided by the number of cases.
Assume, for example, that you want to know the moments for a population. Because you are computing the moments from sample values, you must consider several corrections. This process leads to many formulas for assessing the skewness, wherefore the IDAX.SKEWNESS_AGG function follows a midway policy. It divides the estimated central moments by the number of cases minus 1. If a value is missing, the whole row is ignored.
Parameter descriptions
- x
- Mandatory.
Returned information
DOUBLE the skewness value of the input variable.
Example
SELECT IDAX.SKEWNESS_AGG(UNIT_COST) from GOSALES.ORDER_DETAILS;